Finite Group Databasebeta

← C103×#9284 #39914559

Subgroups — C103×#9284 #39914559

Order 26368.

396 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3228C211yesmaximal, characteristic
2C103×#2985C211yesmaximal, characteristic, complemented
3C103×#1531C211yesmaximal, characteristic, complemented
4C103×#1530C211yesmaximal, characteristic
5C103×#1496C211yesmaximal, characteristic
6C103×#1287C211yesmaximal, characteristic, complemented
7C103×#1275C211yesmaximal, characteristic, complemented
8#533×C103C2211yescharacteristic
9#532×C103C2211yescharacteristic
10#500×C103C411yescharacteristic
11#498×C103C411yescharacteristic
12#486×C103C411yescharacteristic
13#486×C103C411yescharacteristic
14#482×C103—22no—
15#478×C103—22no—
16#446×C103—22no—
17#446×C103—21no—
18C8×Q8×C103—21no—
19#433×C103—22no—
20#432×C103C2211yescharacteristic
21#432×C103C2211yescharacteristic
22#431×C103C2211yescharacteristic
23#431×C103C2211yescharacteristic
24C2×#97×C103C2211yescharacteristic
25#330×C103—22no—
26#329×C103—22no—
27D4⋊C8×C103—21no—
28D4⋊C8×C103—21no—
29C2×#41×C103—21no—
30C22×C8×C103—21no—
31C4⋊Q8×C103C2×C411yescharacteristic
32C4⋊Q8×C103C2×C411yescharacteristic
33C4⋊Q8×C103C2×C411yescharacteristic
34#127×C103C2×C411yescharacteristic
35#125×C103D412yes—
36#124×C103—21no—
37C22⋊Q8×C103—21no—
38C22⋊Q8×C103—21no—
39#121×C103—21no—
40#121×C103—21no—
41C4×Q8×C103—21no—
42C4×Q8×C103—21no—
43C4×D4×C103—21no—
44C4×D4×C103—21no—
45#117×C103D412yes—
46C2×C42×C103C2311yescharacteristic
47#107×C103—22no—
48#106×C103—22no—
49C4⋊C8×C103—22no—
50C4⋊C8×C103—22no—
51C4⋊C8×C103—21no—
52C4⋊C8×C103—21no—
53C4⋊C8×C103—21no—
54C4⋊C8×C103—21no—
55#102×C103—22no—
56#102×C103—22no—
57C22⋊C8×C103—21no—
58C22⋊C8×C103—21no—
59C22⋊C8×C103—21no—
60C22⋊C8×C103—21no—
61#97×C103—22no—
62#97×C103—21no—
63#97×C103—21no—
64#97×C103—21no—
65#97×C103D412yes—
66C4×C8×C103—22no—
67C4×C8×C103C2×C411yescharacteristic
68C4×C8×C103C2×C411yescharacteristic
69C4×C8×C103D411yescharacteristic
70C4×C8×C103D411yescharacteristic
71#41×C103—82no—
72C2×Q8×C103—21no—
73C2×Q8×C103—21no—
74C2×Q8×C103—21no—
75C2×D4×C103—21no—
76C2×D4×C103—21no—
77C2×D4×C103—21no—
78C2×D4×C103—41no—
79C22×C4×C103—41no—
80C22×C4×C103C2×D411yescharacteristic
81C22×C4×C103#4111yescharacteristic
82C22×C4×C103#4111yescharacteristic
83C2×C8×C103—22no—
84C2×C8×C103—21no—
85C2×C8×C103—21no—
86C2×C8×C103—21no—
87C2×C8×C103—22no—
88C2×C8×C103—21no—
89C2×C8×C103—41no—
90C2×C8×C103—41no—
91C2×C8×C103—41no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103—22no—
95C4⋊C4×C103—22no—
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103C22⋊C412yes—
99C4⋊C4×C103C22⋊C412yes—
100C22⋊C4×C103—22no—
101C22⋊C4×C103—41no—
102C22⋊C4×C103—41no—
103C42×C103—22no—
104C42×C103C22×C411yescharacteristic
105C42×C103C2×D411yescharacteristic
106C42×C103C2×D411yescharacteristic
107C42×C103C2×D411yescharacteristic
108C23×C103—41no—
109C23×C103#12311yescharacteristic
110Q8×C103—41no—
111Q8×C103—41no—
112Q8×C103—81no—
113Q8×C103—81no—
114D4×C103—42no—
115D4×C103—41no—
116D4×C103—41no—
117D4×C103—81no—
118D4×C103—82no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—22no—
122C2×C4×C103—22no—
123C2×C4×C103—41no—
124C2×C4×C103—41no—
125C2×C4×C103—41no—
126C2×C4×C103—82no—
127C2×C4×C103C2×C22⋊C411yescharacteristic
128C2×C4×C103C4×D411yescharacteristic
129C2×C4×C103C4×D411yescharacteristic
130C2×C4×C103#12011yescharacteristic
131C2×C4×C103#12111yescharacteristic
132C2×C4×C103#12111yescharacteristic
133C8×C103—41no—
134C8×C103—42no—
135C8×C103—41no—
136C8×C103—41no—
137C8×C103—41no—
138C8×C103—42no—
139C8×C103—81no—
140C22×C103—21no—
141C22×C103—21no—
142C22×C103—21no—
143C22×C103—81no—
144C22×C103—81no—
145C22×C103—81no—
146C22×C103#38611yescharacteristic
147C4×C103—21no—
148C4×C103—21no—
149C4×C103—21no—
150C4×C103—21no—
151C4×C103—21no—
152C4×C103—42no—
153C4×C103—42no—
154C4×C103—81no—
155C4×C103#44311yescharacteristic
156C4×C103#44411yescharacteristic
157#9284C10311yesmaximal, characteristic, direct product factor, Sylow
158C2×C103—41no—
159C2×C103—161no—
160C2×C103#187611yescharacteristic
161C2×C103#190311yescharacteristic
162C2×C103#191211yescharacteristic
163#3228C2×C10311yescharacteristic
164#2985C2×C10311yescharacteristic, complemented
165#1531C2×C10311yescharacteristic, complemented
166#1530C2×C10311yescharacteristic
167#1496C2×C10311yescharacteristic
168#1287C2×C10311yescharacteristic, complemented
169#1275C2×C10311yescharacteristic, complemented
170C103#928411yescharacteristic, direct product factor, Sylow
171#533C22×C10311yescharacteristic
172#532C22×C10311yescharacteristic
173#500C4×C10311yescharacteristic
174#498C4×C10311yescharacteristic
175#486C4×C10311yescharacteristic
176#486C4×C10311yescharacteristic
177#482—22no—
178#478—22no—
179#446—22no—
180#446—21no—
181C8×Q8—21no—
182#433—22no—
183#432C22×C10311yescharacteristic
184#432C22×C10311yescharacteristic
185#431C22×C10311yescharacteristic
186#431C22×C10311yescharacteristic
187C2×#97C22×C10311yescharacteristic
188#330—22no—
189#329—22no—
190D4⋊C8—21no—
191D4⋊C8—21no—
192C2×#41—21no—
193C22×C8—21no—
194C4⋊Q8C2×C4×C10311yescharacteristic
195C4⋊Q8C2×C4×C10311yescharacteristic
196C4⋊Q8C2×C4×C10311yescharacteristic
197#127C2×C4×C10311yescharacteristic
198#125D4×C10312yes—
199#124—21no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202#121—21no—
203#121—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×D4—21no—
207C4×D4—21no—
208#117D4×C10312yes—
209C2×C42C23×C10311yescharacteristic
210#107—22no—
211#106—22no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218#102—22no—
219#102—22no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224#97—22no—
225#97—21no—
226#97—21no—
227#97—21no—
228#97D4×C10312yes—
229C4×C8—22no—
230C4×C8C2×C4×C10311yescharacteristic
231C4×C8C2×C4×C10311yescharacteristic
232C4×C8D4×C10311yescharacteristic
233C4×C8D4×C10311yescharacteristic
234#41—82no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C22×C4—41no—
243C22×C4C2×D4×C10311yescharacteristic
244C22×C4#41×C10311yescharacteristic
245C22×C4#41×C10311yescharacteristic
246C2×C8—22no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4C22⋊C4×C10312yes—
262C4⋊C4C22⋊C4×C10312yes—
263C22⋊C4—22no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42—22no—
267C42C22×C4×C10311yescharacteristic
268C42C2×D4×C10311yescharacteristic
269C42C2×D4×C10311yescharacteristic
270C42C2×D4×C10311yescharacteristic
271C23—41no—
272C23#123×C10311yescharacteristic
273Q8—41no—
274Q8—41no—
275Q8—81no—
276Q8—81no—
277D4—42no—
278D4—41no—
279D4—41no—
280D4—81no—
281D4—82no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—82no—
290C2×C4C2×C22⋊C4×C10311yescharacteristic
291C2×C4C4×D4×C10311yescharacteristic
292C2×C4C4×D4×C10311yescharacteristic
293C2×C4#120×C10311yescharacteristic
294C2×C4#121×C10311yescharacteristic
295C2×C4#121×C10311yescharacteristic
296C8—42no—
297C8—41no—
298C8—42no—
299C8—41no—
300C8—41no—
301C8—41no—
302C8—81no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#386×C10311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—81no—
318C4#443×C10311yescharacteristic
319C4#444×C10311yescharacteristic
320C2—41no—
321C2—161no—
322C2C103×#187611yescharacteristic
323C2C103×#190311yescharacteristic
324C2C103×#191211yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radical#532×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C103×#2985C2semidirect
3. C103×#1531C2semidirect
6. C103×#1287C2semidirect
7. C103×#1275C2semidirect
157. #9284C103direct (N × H)
164. #2985C2×C103semidirect
165. #1531C2×C103semidirect
168. #1287C2×C103semidirect
169. #1275C2×C103semidirect
170. C103#9284direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C103×#32282
C103×#29852
C103×#15312
C103×#15302
C103×#14962
C103×#12872
C103×#12752
#9284103